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A capacitor of capacitance C = 7.5 μF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 11.5 kΩ, and a battery which provides a potential difference of VB = 110 V (a) Calculate the current I a very long time after the switch has been closed in A. (b) Calculate the time t after which the current through the resistor is one-third of its maximum value in s. (c) Calculate the charge Q on the capacitor when the current in the resistor equals one third its maximum value in C

A capacitor of capacitance C = 7.5 μF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 11.5 kΩ, and a battery which provides a potential difference of VB = 110 V (a) Calculate the current I a very long time after the switch has been closed in A. (b) Calculate the time t after which the current through the resistor is one-third of its maximum value in s. (c) Calculate the charge Q on the capacitor when the current in the resistor equals one third its maximum value in C

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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A capacitor of capacitance C = 7.5 μF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 11.5 kΩ, and a battery which provides a potential difference of VB = 110 V

(a)  Calculate the current I a very long time after the switch has been closed in A. 
(b)  Calculate the time t after which the current through the resistor is one-third of its maximum value in s. 
(c) Calculate the charge Q on the capacitor when the current in the resistor equals one third its maximum value in C. 

This diagram represents a basic RC (resistor-capacitor) circuit, which is a fundamental concept in electronics and electrical engineering. Here's a detailed explanation of each component in the circuit: 1. **Resistor (R)** - Symbol: A zigzag line. - Function: A resistor is an electrical component that opposes the flow of current. Its resistance is measured in ohms (Ω). 2. **Capacitor (C)** - Symbol: Two parallel lines, one of which is curved. - Function: A capacitor stores electrical energy in an electric field. Its capacitance is measured in farads (F). 3. **Switch (S)** - Symbol: An angled or tilted line that intersects a straight line. - Function: A switch is a device for making and breaking the connection in an electric circuit. 4. **Battery (Vᴮ)** - Symbol: A pair of parallel lines, one long and one short, which represents the positive and negative terminals respectively. - Function: A battery provides the electromotive force (EMF) or voltage that drives current through the circuit. **Circuit Explanation:** - When the switch \( S \) is closed, current from the battery \( V_B \) flows through the resistor \( R \) and charges the capacitor \( C \). - As the capacitor charges, the voltage across its terminals increases until it equals the voltage of the battery \( V_B \). - The resistor \( R \) controls the charging rate of the capacitor. The charging process follows an exponential curve described by the time constant \( τ \), where \( τ = R \times C \). This time constant represents the time it takes for the capacitor to charge to about 63.2% of the battery voltage \( V_B \). This RC circuit is a basic but essential concept used in various applications such as filtering, timing, and wave shaping in electrical and electronic systems.
Transcribed Image Text:This diagram represents a basic RC (resistor-capacitor) circuit, which is a fundamental concept in electronics and electrical engineering. Here's a detailed explanation of each component in the circuit: 1. **Resistor (R)** - Symbol: A zigzag line. - Function: A resistor is an electrical component that opposes the flow of current. Its resistance is measured in ohms (Ω). 2. **Capacitor (C)** - Symbol: Two parallel lines, one of which is curved. - Function: A capacitor stores electrical energy in an electric field. Its capacitance is measured in farads (F). 3. **Switch (S)** - Symbol: An angled or tilted line that intersects a straight line. - Function: A switch is a device for making and breaking the connection in an electric circuit. 4. **Battery (Vᴮ)** - Symbol: A pair of parallel lines, one long and one short, which represents the positive and negative terminals respectively. - Function: A battery provides the electromotive force (EMF) or voltage that drives current through the circuit. **Circuit Explanation:** - When the switch \( S \) is closed, current from the battery \( V_B \) flows through the resistor \( R \) and charges the capacitor \( C \). - As the capacitor charges, the voltage across its terminals increases until it equals the voltage of the battery \( V_B \). - The resistor \( R \) controls the charging rate of the capacitor. The charging process follows an exponential curve described by the time constant \( τ \), where \( τ = R \times C \). This time constant represents the time it takes for the capacitor to charge to about 63.2% of the battery voltage \( V_B \). This RC circuit is a basic but essential concept used in various applications such as filtering, timing, and wave shaping in electrical and electronic systems.
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